A benchmarking and sensitivity study of the full two-body gravitational dynamics of the DART mission target, binary asteroid 65803 Didymos Harrison Agrusa, Derek Richardson, Alex Davis, Eugene Fahnestock, Masatoshi Hirabayashi, Nancy Chabot, Andrew Cheng, Andrew Rivkin, Patrick Michel To cite this version: Harrison Agrusa, Derek Richardson, Alex Davis, Eugene Fahnestock, Masatoshi Hirabayashi, et al.. A benchmarking and sensitivity study of the full two-body gravitational dynamics of the DART mission target, binary asteroid 65803 Didymos. Icarus, Elsevier, 2020, 349, pp.113849. 10.1016/j.icarus.2020.113849. hal-02986184 HAL Id: hal-02986184 https://hal.archives-ouvertes.fr/hal-02986184 Submitted on 22 Dec 2020 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. A Benchmarking and Sensitivity Study of the Full Two-Body Gravitational Dynamics of the DART Mission Target, Binary Asteroid 65803 Didymos Harrison F. Agrusaa,∗, Derek C. Richardsona, Alex B. Davisb, Eugene Fahnestockc, Masatoshi Hirabayashid, Nancy L. Chabote, Andrew F. Chenge, Andrew S. Rivkine, Patrick Michelf, and the DART Dynamics Working Group aDepartment of Astronomy, University of Maryland, College Park, MD 20742, USA bUniversity of Colorado Boulder, 429 UCB, Boulder, CO 80309, USA cJet Propulsion Laboratory, California Institute of Technology, Pasadena, CA 91109, USA dAuburn University, 39 Davis Hall, Auburn, AL 36849, USA eJohns Hopkins University Applied Physics Laboratory, Laurel MD, 20723, USA fUniversit Cte dAzur, Observatoire de la Cte dAzur, CNRS, Laboratoire Lagrange, 06304 Nice, France Abstract NASA’s Double Asteroid Redirection Test (DART) is designed to be the first demonstration of a kinetic impactor for planetary defense against a small-body impact hazard. The target is the smaller component of the binary asteroid 65803 Didymos. We have conducted high-fidelity rigid full two-body simulations of the mutual dynamics of this system in a broad benchmarking exercise to find the best simulation methodologies, and to understand the sensitivity of the system to initial conditions. Due to the non-spherical shapes of the components and their close proximity, the components cannot be treated as point masses and so the dynamics differ significantly from a simple Keplerian orbit, necessitating the use of numerical simulations to fully capture the system’s dynamics. We find that the orbit phase (angular position or true anomaly) of the secondary is highly sensitive to the initial rotation phase of the primary, making prediction of the secondary’s location from numerical simulation challenging. Finally, we show that the DART impact should induce significant free and forced librations on the secondary. If this libration can be measured by ESA’s recently approved follow-up spacecraft, Hera, it may be possible to constrain properties of the secondary’s interior structure. Keywords: Asteroids, dynamics, Rotational dynamics, Celestial mechanics, Near-Earth objects Preprint submitted to Icarus May 5, 2020 1 1. Introduction 2 The Asteroid Impact & Deflection Assessment (AIDA) collaboration is a NASA- and ESA- 3 supported effort to test the capability of a kinetic impactor for hazardous asteroid mitigation. 4 NASA will lead the Double Asteroid Redirection Test (DART) mission, which will achieve a 5 kinetic impact on the secondary (Didymos B) of 65803 Didymos, a near-Earth binary asteroid, 6 in the fall of 2022 (Cheng et al., 2018). ESA will lead Hera, a follow-up mission to rendezvous 7 with Didymos to characterize the system and visible effects of the impact (Michel et al., 2018). 8 The main goal of the DART mission is to demonstrate the kinetic impactor technique by inter- 9 cepting the secondary, causing a change in the binary orbital period that can be measured with 10 ground-based observations. 11 In this work, we present results from a suite of benchmarking simulations conducted by the 12 DART Investigation Team’s Dynamics Working Group to better understand the complex mutual 13 dynamics, to constrain the sensitivity of the simulated Didymos system to initial conditions, and 14 to identify the appropriate numerical methods to fully capture the dynamics. In Section 1.1 we 15 describe the physical and dynamical properties of the Didymos system. Section 2 introduces the 16 four dynamics models used in this study and the initial conditions of the simulation cases. The 17 results are presented in Section 3. Finally, we discuss future work to better understand the Didymos 18 binary in Section 4. 19 1.1. The Didymos System 20 Discovered in 1996, 65803 Didymos is classified as a near-Earth object and potentially haz- 21 ardous asteroid with a heliocentric semi-major axis of 1:644 au (Alday et al., 1996). In 2003, it 22 was discovered that Didymos is a binary system (Pravec et al., 2003). The binary has a mutual 23 orbit period of Porb ∼ 11:9217 h and a semi-major axis of aorb ∼ 1:19 km (Pravec et al., 2006; 24 Naidu et al., 2020a). According to the binary mean separation and orbital period, Kepler’s third 11 25 law for assumed point masses implies a system mass of Msys ∼ 5:37 × 10 kg. ∗Corresponding author Email address: [email protected] (Harrison F. Agrusa) 2 26 The primary (Didymos A) is ∼780 m across and has an oblate shape and equatorial ridge, and 27 the secondary (Didymos B) is approximately 164 m across and we assume an ellipsoidal shape 28 similar to that of other NEO binary secondaries. Didymos A is a fast rotator, with a spin period 29 of 2:26 h. A polyhedral shape model with 1996 facets was derived by Naidu et al. (2020a) from 30 combined radar and light curve data. In the simulations presented here, Didymos B is assumed to 31 be synchronous (i.e., tidally locked) with its long axis initially aligned with the line of centers. It 32 is also assumed that both bodies are in principal axis rotation and that their spin poles are initially 33 aligned with the binary orbit normal. 34 Table 1 summarizes the relevant physical and dynamical parameters of the Didymos system. 35 These are the nominal system parameters adopted by the DART investigation team at the current 36 time and will be updated throughout the DART mission as new measurements become available. 37 2. Methodology 38 The Didymos binary is an example of the full two-body problem (F2BP), where the rotational 39 and translational dynamics are fully coupled, due to the objects’ irregular shapes and the close 40 proximity of the components. As a result, the system’s dynamical evolution is especially sensitive 41 to the shapes and initial positions and orientations of each component, thus F2BP simulation codes 42 are necessary to fully capture the system’s dynamics. 43 2.1. The Simulation Codes 44 Four different codes were tested in this study, each developed by team members at NASA 45 JPL, University of Colorado Boulder (UCB), Auburn University, and the University of Maryland 46 (UMd), respectively. Only some of these codes have official names, so we refer to each code by 47 the institution that developed it for simplicity. Brief descriptions of the codes are given below. 48 NASA JPL. The JPL code is based on the formulation of the mutual gravitational potential be- 49 tween two polyhedral bodies developed by Werner and Scheeres (2005). It calculates the mutual 50 gravitational potential and its gradients through a Legendre polynomial series expansion, truncated 51 to a desired order, and integrates the discrete-time Hamiltonian equations of motion using the Lie- 52 Group Variational Integrator (LGVI) developed by Lee et al. (2007). This code was written in C++ 3 Symbol Parameter Value Comments/References aorb Semi-major Axis 1:19 ± 0:03 km (Naidu et al., 2020a) c : b : a Secondary Axis Ratios 1:1.2:1.56 Assumed, based on other binary systems. DP Diameter of Primary 780 ± 30 m (Naidu et al., 2020a) DS Diameter of Secondary 164 ± 18 m Derived from DP and DS=DP DS=DP Size Ratio 0:21 ± 0:01 (Scheirich and Pravec, 2009) eorb Binary Orbit eorb < 0:03 Upper limit, assumed zero. (Scheirich and Eccentricity Pravec, 2009) iorb Binary Orbit 0.0 Assumed. Inclination (λ, β) Mutual Orbit Pole (310◦; −84◦) ± 10◦ Ecliptic coordinates, (Scheirich and Pravec, 2009; Naidu et al., 2020a) 11 Msys Total System Mass (5:37 ± 0:44) × 10 kg Derived via Kepler’s 3rd Law with Porb and aorb. Porb Binary Orbit Period 11:9217 ± 0:0002 h One possible orbit solution. (Scheirich and Pravec, 2009) PP Primary Spin Period 2:2600 ± 0:0001 h (Pravec et al., 2006) PS Secondary Spin Period 11:9217 h Assumed. −3 ρP Primary Bulk Density 2170 ± 350 kg m Derived based on DP and Msys. −3 ρS Secondary Bulk 2170 ± 350 kg m Assumed. Density Table 1: Physical and dynamical parameters of the Didymos System. These are the current nominal values adopted by the DART investigation team. Because these parameters are constantly being refined by ongoing observations, these are not exactly the same parameters used in this study. The initial conditions of the simulations presented here differ slightly, but remain within the uncertainty bounds given here. (See Table 3 for the simulation initial conditions.) 4 53 and parallelized to run on a cluster computer environment, due to the high computational cost of 54 the potential and gradients evaluation at each timestep.